Answer to Question #4962 in Mechanics | Relativity for yamini

2011-11-01T13:35:17-0400

Question #4962

6 particles situated at the corners of a regular hexagon of side &#039;a&#039; move at a constant speed &#039;v&#039;. each particle maintains a direction towards the particle at the next corner. the time taken &#039;t&#039; by the particles to meet each other is ?

Expert's answer

2011-11-04T11:42:15-0400

Let us concentrate on two particles say A and B only.Initial separation between two particles = side of the hexagon=aFinal separation =0Thus, relative displacement between two particles =a.Particle B has a component of velocity v cos 60& along ABThus, relative velocity with which A approaches B is v-vcos 60=v/2 As v is uniform& time taken by theese two particles to meet = relative displacement/relative velocity =a/(v/2)=2a/vHence the time taken by particles to meet each other =2a/v - answer<img 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" 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